What kind of transformation converts the graph of f(x) = 2|x - 10| into the graph of g(x) = 2|x - 10| - 3? Choices: (A)translation 3 units up (B)translation 3 units down (C)translation 3 units left (D)translation 3 units right

Compare Functions: To determine the type of transformation from f(x) to g(x), we need to compare the two functions and see how they differ. The function f(x) = 2|x - 10| is being transformed into g(x) = 2|x - 10| - 3. We can see that the only difference between f(x) and g(x) is the subtraction of 3 from the entire function.Identify Difference: Since the subtraction of 3 affects the entire function, it means that every y-value of the graph of f(x) is decreased by 3 to get the corresponding y-value of the graph of g(x). This is a vertical shift.Vertical Shift Down: A vertical shift down by 3 units is represented by subtracting 3 from the function. Therefore, the transformation that converts f(x) into g(x) is a translation 3 units down.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of transformation converts the graph of $f(x) = 2|x - 10|$ into the graph of $g(x) = 2|x - 10| - 3$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units up $\newline$ (B) translation $3$ units down $\newline$ (C) translation $3$ units left $\newline$ (D) translation $3$ units right

View step-by-step help

Home

Math Problems

Precalculus

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 2|x - 10|

into the graph of

g(x) = 2|x - 10| - 3

\newline

Choices:

\newline

(A) translation

3

units up

\newline

(B) translation

3

units down

\newline

3

units left

\newline

(D) translation

3

units right

Compare Functions: To determine the type of transformation from $f(x)$ to $g(x)$ , we need to compare the two functions and see how they differ. The function $f(x) = 2|x - 10|$ is being transformed into $g(x) = 2|x - 10| - 3$ . We can see that the only difference between $f(x)$ and $g(x)$ is the subtraction of $3$ from the entire function.
Identify Difference: Since the subtraction of $3$ affects the entire function, it means that every $y$ -value of the graph of $f(x)$ is decreased by $3$ to get the corresponding $y$ -value of the graph of $g(x)$ . This is a vertical shift.
Vertical Shift Down: A vertical shift down by $3$ units is represented by subtracting $3$ from the function. Therefore, the transformation that converts $f(x)$ into $g(x)$ is a translation $3$ units down.